@book{Jacod2003,
abstract = {This introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.},
author = {Jacod, Jean and Protter, Philip E.},
isbn = {3540438718},
keywords = {SS14 Stochastic analysis},
mendeley-tags = {SS14 Stochastic analysis},
pages = {254},
publisher = {Springer},
title = {{Probability Essentials}},
url = {http://books.google.com/books?id=OK\_d-w18EVgC\&pgis=1},
year = {2003}
}
@book{Karatzas1991,
abstract = {A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.},
author = {Karatzas, Ioannis},
isbn = {0387976558},
keywords = {SS14 Stochastic analysis},
mendeley-tags = {SS14 Stochastic analysis},
pages = {470},
publisher = {Springer},
title = {{Brownian Motion and Stochastic Calculus}},
url = {http://books.google.com/books?id=ATNy\_Zg3PSsC\&pgis=1},
year = {1991}
}
@book{klenke2008wahrscheinlichkeitstheorie,
author = {Klenke, Achim},
file = {:Users/randolfaltmeyer/Dropbox/Notes/On Books$\backslash$:Notes/Klenke\_Wahrscheinlichkeitstheorie.lyx:lyx},
isbn = {9783540775713},
publisher = {Springer London, Limited},
title = {{Wahrscheinlichkeitstheorie}},
url = {http://books.google.it/books?id=bmy89K9VjHIC},
year = {2008}
}
@book{oksendal2010,
abstract = {This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. Apart from several minor corrections and improvements, based on useful comments from readers and experts, the most important change in the corrected 5th printing of the 6th edition is in Theorem 10.1.9, where the proof of part b has been corrected and rewritten. The corrected 5th printing of the 6th edition is forthcoming and expected in September 2010.},
author = {\O ksendal, Bernt Karsten},
isbn = {3642143946},
keywords = {SS14 Stochastic analysis},
mendeley-tags = {SS14 Stochastic analysis},
pages = {384},
publisher = {Springer Science \& Business},
title = {{Stochastic Differential Equations: An Introduction with Applications}},
url = {http://books.google.com/books?id=EQZEAAAAQBAJ\&pgis=1},
volume = {2010},
year = {2010}
}
@book{protter2004stochastic,
author = {Protter, Philip E.},
isbn = {9783540003137},
publisher = {Springer},
series = {Applications of Mathematics},
title = {{Stochastic Integration and Differential Equations: Version 2.1}},
url = {http://books.google.it/books?id=mJkFuqwr5xgC},
year = {2004}
}
@book{Revuz1999,
abstract = {"This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion....This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises." –BULLETIN OF THE L.M.S.},
author = {Revuz, Daniel and Yor, Marc},
isbn = {3540643257},
keywords = {SS14 Stochastic analysis},
mendeley-tags = {SS14 Stochastic analysis},
pages = {602},
publisher = {Springer},
title = {{Continuous Martingales and Brownian Motion}},
url = {http://books.google.com/books?id=1ml95FLM5koC\&pgis=1},
year = {1999}
}
@book{Rogers2000,
abstract = {Now available in paperback, this celebrated book remains a key systematic guide to a large part of the modern theory of Probability. The authors not only present the subject of Brownian motion as a dry part of mathematical analysis, but convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively presentation of the theory of Markov processes. Together with its companion volume, this book equips graduate students for research into a subject of great intrinsic interest and wide applications.},
author = {Rogers, L. C. G. and Williams, David},
isbn = {0521775949},
keywords = {SS14 Stochastic analysis},
mendeley-tags = {SS14 Stochastic analysis},
pages = {406},
publisher = {Cambridge University Press},
title = {{Diffusions, Markov Processes, and Martingales: Volume 1, Foundations}},
url = {http://books.google.com/books?id=eJp330pIvQ4C\&pgis=1},
volume = {4},
year = {2000}
}
@book{Steele2001,
abstract = {The Wharton School course on which the book is based is designed for energetic students who have had some experience with probability and statistics, but who have not had advanced courses in stochastic processes. Even though the course assumes only a modest background, it moves quickly and - in the end - students can expect to have the tools that are deep enough and rich enough to be relied upon throughout their professional careers. The course begins with simple random walk and the analysis of gambling games. This material is used to motivate the theory of martingales, and, after reaching a decent level of confidence with discrete processes, the course takes up the more demanding development of continuous time stochastic process, especially Brownian motion. The construction of Brownian motion is given in detail, and enough material on the subtle properties of Brownian paths is developed so that the student should sense of when intuition can be trusted and when it cannot. The course then takes up the It¿ integral and aims to provide a development that is honest and complete without being pedantic. With the It¿ integral in hand, the course focuses more on models. Stochastic processes of importance in Finance and Economics are developed in concert with the tools of stochastic calculus that are needed in order to solve problems of practical importance. The financial notion of replication is developed, and the Black-Scholes PDE is derived by three different methods. The course then introduces enough of the theory of the diffusion equation to be able to solve the Black-Scholes PDE and prove the uniqueness of the solution.},
author = {Steele, J. Michael},
isbn = {0387950168},
keywords = {SS14 Stochastic analysis},
mendeley-tags = {SS14 Stochastic analysis},
pages = {300},
publisher = {Springer},
title = {{Stochastic Calculus and Financial Applications}},
url = {http://books.google.com/books?id=H06xzeRQgV4C\&pgis=1},
year = {2001}
}
@book{williams1991probability,
author = {Williams, David},
isbn = {9780521406055},
publisher = {Cambridge University Press},
series = {Cambridge mathematical textbooks},
title = {{Probability with Martingales}},
url = {http://books.google.it/books?id=e9saZ0YSi-AC},
year = {1991}
}
@book{rogerswilliams2,
address = {Cambridge},
annote = {It\^{o} calculus,
Reprint of the second (1994) edition},
author = {Rogers, L C G and Williams, David},
isbn = {0-521-77593-0},
keywords = {SDE diffusions markov\_processes reference},
pages = {xiv+480},
publisher = {Cambridge University Press},
series = {Cambridge Mathematical Library},
title = {{Diffusions, Markov processes, and martingales. Volume 2}},
year = {2000}
}